[R] Paired t-tests

[Peter Dalgaard]

Marc Schwartz wrote:
> On Aug 15, 2010, at 9:05 AM, R Help wrote:
> 
>> Hello List,
>>
>> I'm trying to do a paired t-test, and I'm wondering if it's consistent
>> with equations.  I have a dataset that has a response and two
>> treatments (here's an example):
>>
>>   ID trt order          resp
>> 17  1   0     1  0.0037513592
>> 18  2   0     1  0.0118723051
>> 19  4   0     1  0.0002610251
>> 20  5   0     1 -0.0077951450
>> 21  6   0     1  0.0022339952
>> 22  7   0     2  0.0235195453
>>
>> The subjects were randomized and assigned to receive either the
>> treatment or the placebo first, then the other.  I know I'll
>> eventually have to move on to a GLM or something that incorporates the
>> order, but for now I wanted to start with a simple t.test.  My problem
>> is that, if I get the responses into two vectors x and y (sorted by
>> ID) and do a t.test, and then compare that to a formula t.test, they
>> aren't the same.
>>
>>> t.test(x,y,paired=TRUE)
>> 	Paired t-test
>>
>> data:  x and y
>> t = -0.3492, df = 15, p-value = 0.7318
>> alternative hypothesis: true difference in means is not equal to 0
>> 95 percent confidence interval:
>> -0.010446921  0.007505966
>> sample estimates:
>> mean of the differences
>>           -0.001470477
>>
>>> t.test(resp~trt,data=dat1[[3]],paired=TRUE)
>> 	Paired t-test
>>
>> data:  resp by trt
>> t = -0.3182, df = 15, p-value = 0.7547
>> alternative hypothesis: true difference in means is not equal to 0
>> 95 percent confidence interval:
>> -0.007096678  0.005253173
>> sample estimates:
>> mean of the differences
>>          -0.0009217521
>>
>> What I'm assuming is that the equation isn't retaining the inherent
>> order of the dataset, so the pairing isn't matching up (even though
>> the dataset is ordered by ID).  Is there a way to make the t.test
>> retain the correct ordering?
>>
>> Thanks,
>> Sam
> 
> 
> See this thread from just 2 days ago:
> 
>   https://stat.ethz.ch/pipermail/r-help/2010-August/249068.html
> 
> perhaps focusing on Thomas' reply, which is the next post in the thread.
> 
> Bottom line, don't use the formula method for a paired t test.

Yes. I'm not sure the same problem is afoot here, though. In particular,
I'm puzzled by the fact that there are 15DF in both cases, but different
average difference. This kind of suggests to me that maybe the x and y
are not computed correctly. (If only the ordering was scrambled, the
average difference should be the same, but the variance typically
inflated.)

-- 
Peter Dalgaard
Center for Statistics, Copenhagen Business School
Phone: (+45)38153501
Email: pd.mes at cbs.dk  Priv: PDalgd at gmail.com